NEW MATHEMATICAL-MODEL FOR DETERMINING TIME-DEPENDENT ADSORPTION AND DIFFUSION OF DYES INTO FIBERS THROUGH DYE SORPTION CURVES IN COMBINATION SHADES .1. MATHEMATICAL FUNDAMENTALS

Dye uptake of textile substrates can be described as time-dependent by a new mathematical model, in which the sorption process is divided in to fast and slow subprocesses. The fast subprocess describes the adsor ption of the dye onto the fiber surface, and the slow one details the diffusion of the dye into the fiber. In addition, dye desorption is si multaneously considered along with adsorption. Relating this concept t o the dyeing process, it is possible to divide the process into two pa rts-dye adsorption and diffusion. The model is verified by dyeing cott on with direct dyes, but the results are also transferable to other fi bers and dye classes. Using this model, optimum dyeing parameters and dye combinations can be. determined from the sorption curves, which ar e easily obtained by UV-VIS spectrophotometry.